Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively, p and q are equivalent if and only if the columns in a truth table giving their truth values agree.
Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.
let us consider,
T be the truth and F be the false of a problem statement.
Then the compound propositions p and q are logically equivalent if :
P q P→q
T T T
F F T
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The complete question is :
What is the correct way of determining of two compound propositions p and q are equivalent.
construct a truth table for p→q if the proposition is tautology.
Find the point on the curve y = -x^2 - 2 that is closest to the point (0, 1). A. (0, 0) B. (0, -2) C. (1, -3) D. (-1, -3)
Answer:
the answer is B (0, -2)
Step-by-step explanation:
To find the point on the curve y = -x^2 - 2 that is closest to the point (0,1), we can use the method of least squares.
The method of least squares involves finding the point on the curve that minimizes the square of the distance between the point and the curve.
To begin, we can define a function d(x) = (y - (-x^2 - 2))^2 which represents the square of the distance between the point (x,y) on the curve and the point (0,1)
then we need to find the derivative of d(x) and set it to zero to find the minimum,
d'(x) = 2(y + x^2 + 2 - 1) = 2(y + x^2 + 1)
by setting d'(x) = 0 we get y = -x^2 - 1,
so the point on the curve that is closest to (0,1) is (0, -1) and the answer is B (0, -2)
Note that the point (0,-1) is on the curve y = -x^2 - 2 but not the point on the closest.
What is the answer to this?
a line segment that connects the center of the circle to any point on the circle
suppose that n people give their hats to a hat-check attendant, who then returns them randomly, one to each person. (thus, all possible re-assignments of hats to people are equally likely). let x be the number of people who receive their own hats back.
x is the probability of people who receive their original hats back out of the n people. All possible re-assignments are equally likely.
x is the number of people out of the n people who are lucky enough to receive their original hats back from the hat-check attendant. All possible re-assignments of hats to people are equally likely. This means that each person has an equal chance of getting their own hat back, and the probability of any particular person getting their own hat back is 1/n. The expected value of x is therefore n/2, since the average of all possible outcomes is the expected value. The variance of x is (n-1)/12, since the variance is the average of the squared differences from the expected value.
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Given the following table with selected values of f (x) and g(x), evaluate f (g(1)).
x –6 –4 1 3 4
f (x) 4 –1 –6 1 3
g(x) 1 4 3 –4 –6
Check the picture below.
Select the two values of x that are roots of this equation.
x2 + 2x – 6 = 0
A. x = -1 - sqrt of 7
B. x = -1 + sqrt of 7
C. x = -1 +2 sqrt of 7
D. x = -1 -2 sqrt of 7
The solution of the quadratic equation is obtained as -1 ± √7. Option A and B.
What is a quadratic equation?We know that a quadratic equation has to do with the kind of equation that have the general form; y = ax^2 + bx + c. This implies that we are going to have the highest power of the variable to be x.
As such, we have the equation that have been written as; x^2 + 2x – 6 = 0. We are to find the roots of the quadratic equation which are the values for x. When we solve the quadratic equation we have;
-1 ± √7
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Find the slope between the points (8,4) and (2,8)
please help me with this math
PART 1: The solution of the inequality is x < 3.5 and the second graph shows the solution.
PART 2: The inequality she solved is (2/5)x - 4/5 ≤ 1 1/5.
How to solve inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
PART 1
First, solve for x in 9.5x -1.25 < 32
9.5x -1.25 < 32
9.5x < 32 + 1.25
9.5x < 33.25
x < 33.25/9.5
x < 3.5
Since x < 3.5, the circle of the graph will not be shaded. Thus, the second graph is the graph of x < 3.5.
PART 2
The graph of the inequality shown there is x ≤ 5. Thus, any inequality which when solved will give x ≤ 5 will be the inequality that represent the graph.
Let's try (1/5)x - 3/5 ≤ 1/5 and see:
(1/5)x - 3/5 ≤ 1/5
(1/5)x ≤ 1/5 + 3/5
(1/5)x ≤ 4/5
x ≤ 4
This is not the inequality
Let's try (2/5)x - 4/5 ≤ 1 1/5:
(2/5)x - 4/5 ≤ 1 1/5
(2/5)x - 4/5 ≤ 6/5
(2/5)x ≤ 6/5 + 4/5
(2/5)x ≤ 2
2x ≤ 10
x ≤ 5
This is the inequality
Thus, she solved (2/5)x - 4/5 ≤ 1 1/5
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Magan went shopping for a new camera because of a sale. The price on the tag was $21, but Magan paid $12.60 before tax. Find the percent discount.
Answer:
40%
Step-by-step explanation:
To find the percent discount, take the original price and subtract the discounted price.
21 - 12.60=8.4
Divide this by the original price.
8.4/21 = .4
Change this to percent form.
.4 = 40%
Answer:
8.4
Step-by-step explanation:
The price of a bag = 21
Magan paid 12.60
00. 21
12.00
- - - - - - - - -
8.4
If x^2+1/x^2 =1, then what is x^3+1/x^3
Answer:
x^3+1/x^3 = x^2
Step-by-step explanation:
If x^2+1/x^2 =1
The equation x^2+1/x^2 =1 states that the sum of the square of x and the reciprocal of x squared is equal to 1. We can multiply both sides of this equation by x(x+1/x) which is x^2 + 1.
This gives us (x^2)(x+1/x) = x^3 + 1/x^3 = 1.
So, x^3+1/x^3 = x^2.
that x^2+1/x^2 =1, we can deduce that x^3+1/x^3 = x^2. This is because we multiplied both sides of the first equation by x^2 + 1/x^2,
which is equal to x^3+1/x^3 = x^2
Hi, please help me with this, i will be giving brainly and 5 stars once i submit and make sure everything is correct. thanks!
Answer:
see below
Step-by-step explanation:
every stage is 60m
stage one = -340+60 = -280
stage 2: -280 +60 = -220
stage 3: -220 +60 = -160
stage 4: -160+60 = -100
stage 5: -100+60= -40
stage 6: -40+60 =20
it'll take it 6 stages to fully surface
Part 1 A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=−16t2+v0t. Find the time(s) that the projectile will (a) reach a height of 160 ft and (b) return to the ground when v0 is 32 feet per second. Question content area bottom Part 1 (a) Find the time(s) that the projectile will reach a height of 160 ft when v0=32 feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a) The projectile cannot reach a height of 160 feet under given conditions.
b) The projectile takes a time of 2 second to hit the ground.
How to analyze the height of a projectile in time
In this question we find the case of a project under free fall, that is, a vertical uniformly accelerated motion due to action of gravity, whose formula is shown below:
s = - 16 · t² + v₀ · t
Where:
t - Time, in secondsv₀ - Initial speed, in feet per second.Part A - If we know that v₀ = 32 ft / s and s = 160 ft, then the time associated is:
- 16 · t² + v₀ · t - s = 0
- 16 · t² + 32 · t - 160 = 0
By quadratic formula:
t₁ = 1 + i 3, t₂ = 1 - i 3
It is physically impossible to reach a height of 160 feet under conditions given.
Part B - If we know that s = 0 ft and v = 32 ft / s, then the final time is:
- 16 · t² + v₀ · t - s = 0
- 16 · t² + 32 · t = 0
- 16 · t · (t - 2) = 0
The final time for the projectile is 2 seconds.
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solve the system using either gaussian elimination with back-substitution or gauss-jordan elimination. (if there is no solution, enter no solution. if the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.) 3x 3y 12z
So, the solution is x = 1, y = -1, z = 3.
One way to solve the system is using Gaussian elimination with back-substitution. The steps are:
1. Rewrite the system in matrix form, called the augmented matrix:
[3 3 6 | 9]
[1 1 2 | 3]
[2 5 10| 15]
[-1 2 4 | 6]
2. Perform row operations to convert the matrix to an upper triangular matrix.
[1 1 2 | 3]
[0 2 4 | 3]
[0 2 6 | 6]
[0 0 -2 | -6]
3. Use back-substitution to find the values of the variables. Starting with the last equation:
-2z = -6 => z = 3
4y + 6(3) = 6 => y = -1
x + 2(-1) + 2(3) = 3 => x = 1
So, the solution is x = 1, y = -1, z = 3.
Another way is Gauss-Jordan elimination, it's similar with Gaussian elimination but it will change the matrix to a row echelon matrix and then to a reduced row echelon matrix.
So, the solution is x = 1, y = -1, z = 3.
Complete Question: solve the system using either gaussian elimination with back-substitution or gauss-jordan elimination. (if there is no solution, enter no solution. if the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.) 3x + 3y + 6z = 9
x + y + 2z = 3
2x + 5y + 10z = 15
−x + 2y + 4z = 6
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tom and jerry have one day to work, but two tasks to focus on: building chairs and tables. if tom spends all day building chairs, he will make 16 chairs. if he instead devotes his day to building tables, tom will make 4 tables. if jerry spends his day building chairs, he will make 14 chairs; if he spends the day building tables, he will make 7 tables. based on their production possibilities frontiers, tom and jerry:
As per the unitary method, there are 10 chairs and there are 2 tables.
In math the term called unitary method is known as a process of finding the value of a single unit, and based on this value we can find the value of the required number of units.
Here we have given that tom and jerry have one day to work, but two tasks to focus on building chairs and tables.
Here we also know that if tom spends all day building chairs, then he will make 16 chairs.
And if he instead devotes his day to building tables, then tom will make 4 tables.
Where as if jerry spends his day building chairs, then he will make 14 chairs on the other hand if he spends the day building tables, then he will make 7 tables.
Based on the given details, here by using the unitary method, for one day, he will product 10 chairs and 2 tables.
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Match the given differential equation with one or more of the solutions. (Select all that apply.)
xy'' ? y' = 0
y=0
y=2x
y=2x^2
y=2
The solutions that match the given differential equation are a)y=0 and b)y=2x.
The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.
In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.
Therefore, the general solution to this differential equation is y = c1 + c2x.
y=0 is a solution of the differential equation since it satisfies the equation when plugged in.
y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.
y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.
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Question 2 of 8 QUESTION: What is 3/4÷4/5?
Solve the system of equations: 3 � - � = 17 5 � + 3 � = 5 (-4, 5) (4, -5) (-4, -5) (4, 5)
Answer: To solve the system of equations, we can use the substitution method. We'll start by isolating one of the variables in one of the equations.
The first equation is 3x - 2y = 17
We can solve for x by adding 2y to both sides:
3x = 17 + 2y
x = (17 + 2y)/3
We can substitute this expression for x into the second equation:
5((17 + 2y)/3) + 3y = 5
Simplifying, we get:
50 + 10y + 3y = 5
13y = -45
y = -3.5
Now we can substitute this value of y into the equation we found earlier for x:
x = (17 + 2(-3.5))/3
x = (17 - 7)/3
x = 10/3
x = 3.333
So the solution of the system of equations is (x,y) = (3.333, -3.5)
Which is not in the options provided, so the answer is no solution.
Step-by-step explanation:
3x+2=4; 2x-y=5 solve the system of equations algebraically using substitution
this is ur answer.
written by me
I am also class 10 student
Solve for the first variable in one of the equations, then substitute the result into the other equation.Point Form:(2,−1)(2,-1)Equation Form:x=2,y=−1
so the sanswer is 19
—
3.
1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]
To lose the least amount of money in the sales promotion, you should order the minimum number of hats and pairs of sunglasses while still satisfying the constraints given.
Let x be the number of hats you order and y be the number of pairs of sunglasses you order.
From the information given, we can set up the following constraints:
y = 2x (because you will sell at least twice as many hats as pairs of sunglasses)
y <= 100 (because your supplier tells you that your order of sunglasses cannot exceed 100 pairs)
x + y >= 210 (because you estimate that you should order at least 210 items in all)
We also know that you will lose $3 on every hat and $2 on every pair of sunglasses sold. So the objective is to minimize the cost:
Cost = 3x + 2y
Now we can use the constraints to set up a linear optimization problem. We can use a solver to minimize the cost and find the optimal values of x and y that meet the constraints.
Solving the problem gives us x = 140, and y = 280, so you should order 140 hats and 280 pairs of sunglasses to lose the least amount of money in the sales promotion.
culate absolute and relative change
Question
Upon returning from military deployment, Joseph is trying to describe to his family all that has changed at home w
was away. To illustrate his point, he gathered information about common items that had changed in his absence..
found that the average television size was 40.4 inches at the time of his deployment, and was 42.8 inches by the
returned. What is the absolute and relative change in average television sizes from the time of Joseph's deployme
time he returned?
Round your answer for relative change to the nearest hundredth of a percent.
Do not round until your final answer.
Provide your answer below:
The absolute change in average television sizes from the time of Joseph's deployment time he returned is given as follows:
2.4 inches.
The relative change is given as follows:
5.94%.
How to obtain the absolute and the relative change?The absolute change is given by the absolute value of the difference of the final value by the initial value, hence:
|42.8 - 40.4| = 2.4 inches.
The relative change is given by the division of the absolute change by the initial measure, and then multiplied by 100%, hence:
2.4/40.4 x 100% = 5.94%.
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Find the value of x PLEASE I NEED HELPP
Answer:
x =~ 21.93
Step-by-step explanation:
x = hypotenusa
x² = (18 / 2)² + 20²
x² = 9² + 400
x² = 81 + 400
x² =~ 481
x = [tex]\sqrt{481}[/tex]
x =~ 21.93
A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of 0 feet. She descends 21.4 feet. She then travels directly up 5.8 feet. Next, she descends a second time, 36.2 feet. How many feet must she now rise to get back to sea level?
True/False: If the angular diameter of an observed object can be measured and its distance is known, its true physical diameter can be calculated.
If the angular diameter of an observed object can be measured and its distance is known, its true physical diameter can be calculated, and the given statement is TRUE.
An angular distance describes how large a sphere or circle appears from a given point of view.
The angular diameter is calculated as:
Angular Diameter=206265X(Actual diameter/Distance)
The angular diameter of an object is the angle the object makes as seen by an observer. This is demonstrated in the diagram below, where the angular diameter of the object appears larger to an observer at A than to an observer at B.
Angular diameter can also refer to the distances between two objects, measured on the celestial sphere.
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Given the information below, match the step with the reason it can be stated.
Answer:
1. e its given
2. d
3. b
4. c
5. a
this all are proved by the theorem
I need an answer to this question by Tuesday,
(x+5)^2 ; x=-2 and y=1
Answer:
9
Step-by-step explanation:
(-2+5)^2
3^2
9
You are going to conduct coin toss experiment using fair; evenly balanced coin. Answer the following questions regarding your experiment: Hint: You may find it valuable to write out the sample space of the experiment: What is the probability of tossing "heads" on your first coin toss? 0.50 What is the probability of tossing "heads" on each of your first two tosses?
The probability of tossing "heads" on each of your first two tosses is 0.25
Probability = n(E)/n(S)
Where E is the possibility of an event occurring
and S is the sample space i.e., the total number of possible outcomes.
Probability is the measure of how likely an event can happen. The probability of any event lies between 0 and 1 only.
The sample space for when you toss one coin is - H, T
So the probability to get an H is= 1/2
=0.5
Similarly, The sample space for when you toss two coins is HH, TT, HT, TH
So, the probability to get an H on each of your first two tosses is = 1/4
=0.25
Therefore, The probability of tossing "heads" on each of your first two tosses is 0.25
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Is the federal reserve making nickel’s with a constant of proportionality? If so what is it?
What is ratio?
A ratio is a way of comparing two or more values or quantities. It expresses the relationship between the size of one value or quantity to the size of another. Ratios are often written as fractions or as ":".
The Federal Reserve is making nickels with a constant of proportionality. This can be determined by analyzing the relationship between the amount of nickels made and the time elapsed. If the number of nickels made is directly proportional to the time elapsed, then the ratio between the number of nickels made and the time elapsed will be constant.
As we can see from the table, the ratio between the number of nickels made and the time elapsed is constant, which is 6000 nickels per hour. This means that the Federal Reserve is making nickels with a constant of proportionality.
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The Federal Reserve is making nickels with a constant of proportionality.
What is ratio?
A ratio is a way of comparing two or more values or quantities. It expresses the relationship between the size of one value or quantity to the size of another. Ratios are often written as fractions or as ":".
The Federal Reserve is making nickels with a constant of proportionality. This can be determined by analyzing the relationship between the amount of nickels made and the time elapsed. If the number of nickels made is directly proportional to the time elapsed, then the ratio between the number of nickels made and the time elapsed will be constant.
As we can see from the table, the ratio between the number of nickels made and the time elapsed is constant, which is 6000 nickels per hour. This means that the Federal Reserve is making nickels with a constant of proportionality.
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1.234, 1.244 , and 1.247 from greatest to least?
The arrangement with descending trend is 1.247,1.244,1.234
What is a decimal number?A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.
Given here: The decimal numbers 1.234,1.244,1.247
Now If one decimal in the list has a higher whole number than the others, it’s automatically the greatest number. If a decimal in the list has a smaller whole number than the others on the list, it’s automatically the smallest number. . Create enough rows and columns for all of the digits and number spaces (including the decimal point). Going from left to right, label the columns as tens, ones, decimal, tenths, hundredths, and thousandths.
Thus,
ones decimals tenths Hundreths thousands
1 . 2 3 4
1 . 2 4 4
1 . 2 4 7
∴ The order from greatest to least is 1.247,1.244,1.234
Hence, The arrangement with the descending trend is 1.247,1.244,1.234
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how many integers greater than 5400 have both of the following properties? (a) the digits are distinct. (b) the digits 2 and 7 do not occur.
There are 15120 integers greater than 5400 that have distinct digits and do not contain 2 and 7.
The number of required integers is the number of integers greater than 5400 which have distinct digits and do not contain 2 and 7. This can be calculated with the formula:
Number of Required Integers = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) - (2 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 30240 - 15120 = 15120.
This is because for the first part of the equation, we must calculate the total number of possible permutations of distinct digits from 0-9 (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1). For the second part, we must calculate the number of permutations of digits from 0-9 excluding 2 and 7 (2 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1). We then subtract the second part from the first to get the required answer.
Therefore, there are 15120 integers greater than 5400 that have distinct digits and do not contain 2 and 7.
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Reason Hugo walksmile from his home to the library on
Monday. He walks mile from his home to the park on Tuesday.
• How much farther does he walk on Monday than on Tuesday?
• Is your answer reasonable? Explain.
The distance travelled on Monday is 1/2 mile more than the distance travelled on Tuesday. Yes, the answer is reasonable, the difference between the two numbers indicates the remaining distance.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.
Given that the distance travelled on Monday is 5/6 miles, and the distance travelled on Tuesday is 1/3 miles.
To find how much more distance is covered on Monday:
x= 5/6 - 1/3
x= 5/6 - 2/6
x= 3/6
x= 1/2
Hence, the distance travelled on Monday is 1/2 mile more than the distance travelled on Tuesday.
Yes, the answer is reasonable because the difference between the two numbers indicates the remaining distance, that is not covered on Tuesday, thus telling us about the extra distance.
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1. A right triangle has one leg that measures 8ft What is the measure of the acute triangle? Assume that the angle is 36⁰
2. A right triangle has one leg that measures 15ft What is the measure of the acute triangle? Assume that the angle is 36⁰
The measure of the other acute angle of the right angled triangle is 54⁰.
Define the term acute triangle?A form of triangle called an acute triangle has acute angles at each of its three internal angles. Triangles with sharp angles are also known as acute triangles. Acute triangles have different side lengths, but their interior angles are always less than 90°.For the stated question:
Length of one side = 8 ft.
Let angle A = 36⁰.
For right angled triangle, Angle B = 90⁰
Then,
∠A + ∠B + ∠C = 180⁰
36⁰ + 90⁰ + ∠C = 180⁰
∠C = 180⁰ - 126⁰
∠C = 54⁰
Thus, the other acute angle is found as 54⁰.
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The correct question is-
1. A right triangle has one leg that measures 8ft What is the measure of the acute triangle? Assume that the angle is 36⁰